A380007 Hexagonal numbers that are sphenic numbers.

66, 190, 231, 435, 561, 861, 946, 1653, 2278, 3655, 4371, 5151, 5995, 6441, 8911, 9453, 10011, 10585, 13366, 15051, 15753, 16471, 20301, 21115, 22366, 22791, 23653, 26335, 32131, 33153, 39621, 40186, 45451, 50403, 54946, 62481, 69751, 72771, 77421, 80601, 83845, 93961, 99235, 102831

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

66 = 2*3*11 is the product of 3 distinct primes and the 6th hexagonal number hex(6) = 6*(2*6-1).
231 = 3*7*11 is the product of 3 distinct primes and the 11th hexagonal number hex(11) = 11*(2*11-1).

Mathematica

semiQ[k_] := FactorInteger[k][[;; , 2]] == {1, 1}; q[k_] := (PrimeQ[k] && semiQ[2*k - 1]) || (PrimeQ[2*k - 1] && semiQ[k]); Table[k*(2*k - 1), {k, Select[Range[250], q]}] (* Amiram Eldar, Jan 08 2025 *)

Crossrefs

Intersection of A000384 and A007304.

Cf. A129521.

Sequence in context: A255102 A202647 A202640 * A074873 A205817 A046393

Adjacent sequences: A379998 A379999 A380000 * A380014 A380015 A380016

Keyword

nonn,new

Author

Massimo Kofler, Jan 08 2025

Status

approved